1. A polynomial function is a function that can be written in the form
f(x)=anxn +an−1xn−1 +an−2xn−2 +...+a2x2 +a1x+a0,
where each a0, a1, etc. represents a real number, and where n is a natural number Here are the steps required for Solving Polynomials by Factoring:
Step 1: Write the equation in the correct form. To be in the correct form, you must remove all parentheses from each side of the equation by distributing, combine all like terms, and finally set the equation equal to zero with the terms written in descending order. Step 2: Use a factoring strategies to factor the problem. Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero. Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side. Example 1 – Solve: 3x3 = 12x
Step 1: Write the equation in the correct form. In this case, we need to set the equation equal to zero with the terms written in descending order. Step 1 Step 2: Use a factoring strategies to factor the problem. Step 2 Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero. Step 3 Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side. Step 4 Example 2 – Solve: x3 + 5x2 = 9x + 45
Step 1: Write the equation in the correct form. In this case, we need to set the equation equal to zero with the terms written in descending order. Step 1 Step 2: Use a factoring strategies to factor the problem. Step 2 Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero. Step 3 Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side. Step 4 Click Here for Practice Problems
Example 3 – Solve: 6x3 – 16x = 4x2
Step 1: Write the equation in the correct form. In this case, we need to set the equation equal to zero with the terms written in descending order. Step 1 Step 2: Use a factoring strategies to factor the problem. Step 2 Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero. Step 3 Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side. Step 4 Click Here for Practice Problems
Example 4 – Solve: 3x2(3x + 4) = 12x(x + 3)
Step 1: Write the equation in the correct form. In this case, we need to remove all parentheses by distributing and set the equation equal to zero with the terms written in descending order. Step 1 Step 2: Use a factoring strategies to factor the problem. Step 2 Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero. Step 3 Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side. Step 4 Click Here for Practice Problems
Example 5 – Solve: 16x4 = 49x2
Step 1: Write the equation in the correct form. In this case, we need to set the equation equal to zero with the terms written in descending order. Step 1 Step 2: Use a factoring strategies to factor the problem. Step 2 Step 3: Use the Zero Product Property and set each factor containing a variable equal to zero. Step 3 Step 4: Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side. Step 4 Click Here for Practice Problems
Let's see what the range of possible values you can have for 1.3540980 if your uncertainty is +/- 2%
2% of 1.3540980 = 0.02 * 1.3540980 = 0.027082
So the lowest possible value for your result is
1.3540980 - 0.027082 = 1.327016
The largest possible result is
1.3540980 + 0.027082 = 1.38117996
Notice that only the 1st 2 digits of the result match which is reasonable since a 2% error means that your result is only accurate to within 1 part in 50.</span>
